In(x+1)+in(x+4)=In(x+9)

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Solution for In(x+1)+in(x+4)=In(x+9) equation: 


Simplifying
In(x + 1) + in(x + 4) = In(x + 9)

Reorder the terms:
nI(1 + x) + in(x + 4) = In(x + 9)
(1 * nI + x * nI) + in(x + 4) = In(x + 9)
(1nI + nxI) + in(x + 4) = In(x + 9)

Reorder the terms:
1nI + nxI + in(4 + x) = In(x + 9)
1nI + nxI + (4 * in + x * in) = In(x + 9)
1nI + nxI + (4in + inx) = In(x + 9)

Reorder the terms:
4in + inx + 1nI + nxI = In(x + 9)

Reorder the terms:
4in + inx + 1nI + nxI = nI(9 + x)
4in + inx + 1nI + nxI = (9 * nI + x * nI)
4in + inx + 1nI + nxI = (9nI + nxI)

Add '-1nxI' to each side of the equation.
4in + inx + 1nI + nxI + -1nxI = 9nI + nxI + -1nxI

Combine like terms: nxI + -1nxI = 0
4in + inx + 1nI + 0 = 9nI + nxI + -1nxI
4in + inx + 1nI = 9nI + nxI + -1nxI

Combine like terms: nxI + -1nxI = 0
4in + inx + 1nI = 9nI + 0
4in + inx + 1nI = 9nI

Solving
4in + inx + 1nI = 9nI

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-1nI' to each side of the equation.
4in + inx + 1nI + -1nI = 9nI + -1nI

Combine like terms: 1nI + -1nI = 0
4in + inx + 0 = 9nI + -1nI
4in + inx = 9nI + -1nI

Combine like terms: 9nI + -1nI = 8nI
4in + inx = 8nI

Combine like terms: 8nI + -8nI = 0
4in + inx + -8nI = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(4i + ix + -8I) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing i to the left, all other terms to the right.

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4i + ix + -8I)' equal to zero and attempt to solve:

Simplifying
4i + ix + -8I = 0

Reorder the terms:
-8I + 4i + ix = 0

Solving
-8I + 4i + ix = 0

Move all terms containing i to the left, all other terms to the right.

Add '8I' to each side of the equation.
-8I + 4i + 8I + ix = 0 + 8I

Reorder the terms:
-8I + 8I + 4i + ix = 0 + 8I

Combine like terms: -8I + 8I = 0
0 + 4i + ix = 0 + 8I
4i + ix = 0 + 8I
Remove the zero:
4i + ix = 8I

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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